Single-cycle optical pulses with a controlled electromagnetic waveform allow to steer the motion of low-energy electrons in atoms, molecules, nanostructures or condensed-matter on attosecond dimensions in time. However, high-energy electrons under single-cycle light control would be an enabling technology for beam-based attosecond physics with free-electron lasers or electron microscopy. Here we report the control of freely propagating keV electrons with an isolated optical cycle of mid-infrared light and create a modulated electron current with a peak-cycle-specific sub-femtosecond structure in time. The evident effects of the carrier-envelope phase, amplitude and dispersion of the optical waveform on the temporal composition, pulse durations and chirp of the free-space electron wavefunction demonstrate the sub-cycle nature of our control. These results create novel opportunities in laser-driven particle acceleration, seeded free-electron lasers, attosecond space-time imaging, electron quantum optics and wherever else high-energy electrons are needed with the temporal structure of single-cycle light.
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